Numerical study on swirl development in supersonic S-shaped pipes with multiple flow turning angles

This study employs direct numerical simulation to investigate supersonic flows in S-shaped pipes with identical curvature and multiple flow turning angles (5°, 10°, and 15°). Comparison with an equivalent single curved pipe is made, which reveals similarities in secondary flow structures and the response of the compressible boundary layer to the wall curvature. Driven by the imbalance between centrifugal forces and pressure gradients, the swirling flow initiates and gradually develops in the first bend of S-shaped pipes, while the second bend attenuates its intensity through partial counteraction of the circumferential flow velocity. As evidenced by the skin friction coefficient, the combined action of adverse pressure gradients and the convex curvature triggers flow separation in the first bend. The wake region downstream of the reattachment point provides favorable spatial conditions for sustaining the primary swirls. An analogous mechanism accounts for the generation of the counter-rotating swirls downstream of the second bend, albeit at a comparatively reduced spatial scale. Quantitative analysis of axial fluxes of angular momentum and linear momentum reveals that the swirl intensity increases with larger flow turning angles. This effect of enhancement is most pronounced within the inner region of the boundary layer, constituting the dominant contribution. The swirl development in S-shaped pipes significantly enhances the mass and energy transport in the flow field, particularly within the boundary layer, with the efficiency scaling positively with the flow turning angle.